A number is first increased by $20\%$ and then decreased by $20\%$. The net change is

A number is first increased by $20\%$ and then decreased by $20\%$. The net change is
  1. $0\%$ (no change)
  2. decrease of $4\%$
  3. increase of $4\%$
  4. decrease of $40\%$

Solution

Net factor $= 1.20 \times 0.80 = 0.96$, i.e., $96\%$ of original. Net change $= -4\%$ (a $4\%$ decrease). Shortcut: $a + b + \dfrac{ab}{100} = 20 - 20 + \dfrac{(20)(-20)}{100} = -4$.

Asked in: IMO

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